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How big is it by a truly quantum measurement?

I am thinking of comparing Science magazines "Breakthrough of the Year" (BYOT) with the Zeilinger buckyball. The BYOT is a piezoelectric mechanical oscillator (PO) the size of the cross section of a human hair. It is placed in a superposition of its ground state and its first excited state. The well known buckyball experiment is a two slit experiment using buckyballs. (A third candidate might be a macroscopic Josephson junction oscillator conducting both ways at once.)

I have made some basic calculations. For instance, the BYOT contains about 10^14 atoms compared to 60 or 72 atoms in the buckyball. By this measure the BYOT is bigger by a factor of about 10^12.

On the other hand, the two slits are separated by 50 to 100 nanometers, or 10^-7 meters. In its first excited state, the top of the BYOT PO moves about 10^-15 meters per cycle, according to my calculations. By this measure the buckyball wins by a factor of about 10^8.

Calculating energy of the moving parts, I find a much closer horserace, but the buckyball is about 100 times bigger.

However, none of these calculations is at all quantum mechanical (QM). ArXiv lists at least five papers proposing truly quantum mechanical measures of the size of a macroscopic Schrodinger cat. The most recent is Lee and Jeong http://arxiv.org/abs/1101.1209 which references the other four. Can someone competent (or expert) in QM apply one or more of these quantum measures to the BYOT and the buckyball and tell me which is larger? TIA. Jim Graber

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The question sounds interesting, could you link to more information and to references on both BYOT and the BB? –  Malabarba Jan 19 '11 at 14:12
    
References: 1.)As already listed by Chad Orzel, the BYOT reference is Nature 464:697-703 (17 March 2010). Also interesting is the News and Views article by Markus Aspelmeyer on pp 685-686, which does refer to the Schroedinger cat issue and states that “the actual displacement between the two motional states of the prepared superposition is on the order of 10^–16 metres — that is, six orders of magnitude smaller than the size of the unit cells of the resonator’s structural lattice.” 2.) The buckyball reference is Am. J. Phys., Vol. 71, No. 4, April 2003. –  Jim Graber Jan 19 '11 at 23:29
    
Define "larger". Number of particles? Physical size? More publicity? Greater scientific impact? One could argue endlessly about what would constitute the "largest" cat. Ferinstance, the superconducting junction paper Chad Orzel referenced has a large number of particles, but - if I remember correctly - the superposition still evolves phase like it was just 2 electrons (a single Cooper pair). As opposed to some ion-trap-quantum-computer cats, which may have only a dozen particles, but the superpostion evolves phase like a dozen-particle object. –  Anonymous Coward Feb 18 '11 at 19:05
    
@Anonymous coward: A interesting question in current research is to find a meaningful definition of larger in this context... –  Frédéric Grosshans Feb 25 '11 at 11:21
    
Schrödinger did not define the special nature of that cat, so feel free to assume a lion or a tiger, what ever my be bigger. –  Georg Mar 4 '11 at 18:36

6 Answers 6

The largest genuine "cat state" sort of experiment I could find, measured by number of particles, was a couple of experiments on superconducting junctions which involved a few billion electrons. I have, of course, misplaced the references, but I believe this arxiv paper is one of them. (Though looking around for the reference also turns up this recent paper arguing the number is far smaller, at most a few thousand.

Note also that the "Breakthrough of the Year" paper (this Nature article) does not actually claim to have made a Schroedinger cat state. They have cooled a mechanical resonator to its ground state, and demonstrated some control over its state, but they haven't done all the work that would need to be done to demonstrate that what they have is a cat state (which would probably involve some sort of interference effects, that being the usual way to demonstrate something being in more than one state). Given what they have done, it's not a big stretch to think that they will eventually do the cat state experiment, but they haven't published that yet.

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From the Nature paper midway between figure 5 and figure 6: “After one-quarter of the first Rabi oscillation, at τ ≈ 1.9 ns, the qubit and the mechanical resonator are entangled in the state |g1  + |e0 .” This is what I took to be the claim for a Schrodinger cat state. I think the arguable part is how macroscopic it is. –  Jim Graber Jan 19 '11 at 23:55
    
Korsbakken et. al <arxiv.org/abs/1003.5294>; Marquardt et. al. <arxiv.org/abs/quant-ph/0609007>; These two references also argue that the size of the cat in the superconducting junctions is much smaller than it naively appears. –  Jim Graber Jan 20 '11 at 0:06
    
The link in my original answer is to the Korsbakken paper in what I thought was an open-access IOP journal, but turns out to be one of the pay ones (bastards). I'm not certain I would call the sentence you quote a claim to have made a cat state-- what they've got is a pair of systems with one quantum of energy between them-- but even if it is, I don't think what they have is conclusive on that count. They really need to do something more to demonstrate that it's a cat state, either some state tomography or some kind of interferometry. –  Chad Orzel Jan 20 '11 at 0:56
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OK, I concede, and I think the original authors also concede that they haven't (yet) fully characterized the quantum state--or in my oversimplification proved that it is a cat state. But I remain under the impression that it is very likely to actually be one. Do you disagree? –  Jim Graber Jan 20 '11 at 4:25
    
I actually expected more controversy about the buckyball experiment: Is it fair to call a two slit experiment a cat state? –  Jim Graber Jan 20 '11 at 4:27

The Dec 17 2011 Science has in its breakthrough of the year a discussion of “The first Quantum Machine.” It is a vibrating device which has some superposition of vibrational states. It is a maybe a sort of Schrodinger cat state.

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Recall that the LIGO noise limit in some frequency bands is given by the Heisenberg position uncertainty of the two multi kg single crystal sapphire mirrors, apparently about 10^-18m. In other words, to lower the noise, the designers are planning to increase the mass of the mirrors from 10 to 40 kg apiece! This is different from the radiation pressure uncertainties which apparently dominate the error budget in other frequency bands. See e.g. elmer.tapir.caltech.edu/cajagwr/pdf/chen.pdf, for several examples of entanglement, squeezing, etc. Check out the first slide for a photo of one of the 10 kg mirrors. To see Heisenberg position uncertainty in an object of this scale is, to me, somehow truly inspiring.

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+1 for LIGO! One small correction: the mirrors are fused silica, not sapphire (which had been considered). –  nibot Mar 17 '12 at 21:00
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Careful, it's not because a measurement is limited by uncertainty relations that a Schrödinger cat is present ! Ligo is amazing but its mirrors are not Schrödinger cats as you would seem to imply. For a "cat" that big, any coupling with the environment would destroy the quantum superposition, very, very quickly. –  Oli Jun 5 '12 at 9:05

I think you're all scratching your heads for nothing, how would you analyze a cat state if the theory is that you can have multiple possible outcomes before observation? Then there's the fact that if you put a clock in a box instead of a cat and the clock is synchronized with a clock outside the box, wait awhile and open the box it will always have the sametime, the synchronized time, so to say that hidden things have multiple outcomes simply because they are hidden is crazyness. The same probabilities will happen whether observed or not.

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He's talking about the largest quantum superposition that has been detected. The cat title was just a whimsical reference. And he's asking within the framework of QM, an experimentally verified theory. It doesn't matter if its crazyness, he wants the answer from that framework. Otherwise all the quantum mechanics questions on this site would be closed as craziness –  Manishearth Mar 16 '12 at 14:56

Dirac answers this question clearly on the superposition page-- www.enotes.com/topic/quantum_superposition. The issue is not "multiple possible outcomes before observation"--- all possible outcomes exist simultaneously, the one that materialises is the most probable one in terms of your observation, decision or measurement. A simple example from the everyday classical world is as follows--I might look at the refrigerator, and decide it might stop working because it is making a buzzing noise, I might then decide its not level, so I go and get the spirit level and level it----this is the outcome of me looking at the refrigerator but before I make a decision there is an infinite number of ways I could look at the refrigerator, I could decide I need a beer, so I go to the refrigerator and get a beer... ect., ect., ie I could decide many other things related to the refrigerator. Some people call this "the collapse of the wave function" ie there are an infinite number of wave functions existing between me and the refrigerator, but the wave function eventually collapses into a single wave function once I make a decision or measurement. The single wave function is my action, or observation. This has profound metaphysical implications, if thought about deeply. We're in good company---Einstein also posed the question "do you really believe that the moon does not exist when you are not looking at it?"--Einstein is here referring to the "superposition principle", later defined clearly by Dirac. albeit somewhat mathematically, ie the moon exists in an infinite variety of states until observed or measured. Bohr's reply to Einstein on such issues was-- "Einstein, do not tell God what to do"--see Bohr-Einstein letters, or Wikipedia page "Bohr-Einstein debates".

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link is broken :S –  Emilio Pisanty Jun 5 '12 at 10:13

There has just been a paper published on the Arxiv, Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu (summary here), that reports the current record as of November 2013.

The authors have made roughly spherical polymers of molecular weight about 10,000 by tacking fluorinated side chains onto a porphirin core, and they've managed to observe an interference pattern in a Young's slits experiment.

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